Conjecture: “If the successive
(increasing & odd)
primes are subtracted from an even number, and the number of trials needed
to obtain another prime is divided for the square of the natural logarithm
of the even number , this relation taken from the case of large number of
primes subtracted, it is bounded by a constantas the even numbers grows
to infinite”

Example: Be 1077422 an even number. If
we subtract the primes 3,5,7,11...599 from that number, the remainders are
composite numbers. Only when the subtrahend attains 601 then the remainder
results a prime = 1076811.

The number of trials is precisely the
rank of 601 in the sequence of primes, that is 109. Relation = 109 /
(log(1077422))^2 = 0.565. We will call this relation Quality Index.

The plausibility of the conjecture
written above is based in the following data, extracted from the works of
Sinisalo, Deshouillers, Te Riele, Saouter,
Richstein and T. Oliveira (*)

Rodríguez provides the following Table
that summarizes the empirical search done around this issue.

LARGE NUMBER OF TRIALS NEEDED TO
PRODUCE A PRIME DIFFERENCE WHEN THE SUCCESSIVE PRIMES ARE
SUBTRACTED FROM EVEN NUMBERS

Enoch Haga and
Farideh Firoozbakht helped to correct some minor typos in the original
Table sent by Rodríguez. I have incorporated these corrections to
the Table above in order not to handle two Tables.

***

Here is a contribution from Didier van der Straten from Belgium
(April, 2005):

I am just an amateur, interested in every
recent finding about Goldbach conjecture.

I made several math researches, using small
figures, after what I suspected a good direction was to investigate

"gaps between Goldbach partitions".

Then I fell on your text Conjecture 36 by
Sinisalo-Ludovicus, and the questions which seem to remain outstanding.

I soon realised that my study would need to
go to that sort of order of magnitude to realise any progress.

I am working at that. So any data about
those gaps is of interest for me. That includes the initial gap before
reaching a minimal partition.

Meanwhile I kept searching about Goldbach
and I found a page which is in line with sbj conjecture annd its
questions

From Tomas Oliveira : http://ieeta.pt/~tos/goldbach.html
we have this new value.
Even number = 906,030,579,562,279,642
Rank of prime subtracted = 1156
Quality Index = 0.6761
Authors = Fettig & Sobh
All even numbers less than 4x10^18 has been
tested. Date 12-25-2008